1. Field of the Invention
The present invention generally relates to an image pickup system and, more particularly, to an image pickup system having an image reproducing means for correctly reproducing degraded image data in, e.g., an image pickup system such as an electronic still camera for picking an original image to reproduce the original image.
2. Description of the Related Art
As is known, in an imaging system such as an electronic still camera using an optical system, as shown in FIG. 3A, an original image f(r) (r represents a position) is formed on an image pickup element (not shown) through an optical system L as an observation image g(r).
In this case, when the Fourier spectrum of the original image f(r) is represented by F(.omega.), and the Fourier spectrum of the observation image g(r) is represented by G(.omega.), the following equation can be obtained: EQU G(.omega.)=H(.omega.).times.F(.omega.) (1)
(where .omega.: spatial frequency)
In equation (1), H(.omega.) is called an OTF (Optical Transfer Function), and is used for representing image forming characteristics of an imaging system.
In addition, when H(.omega.) is subjected to inverse Fourier transformation, a PSF (Point Spread Function) is obtained.
In order to cause the observation image g (r) to coincide with the original image f(r), H(.omega.)=1 must be satisfied for all spatial frequencies .omega..
However, in a practical optical system, H(.omega.)&lt;1 is satisfied, and a degraded image is formed.
A method using an inverse filter is known as a method of reproducing an original image from an observation image.
The inverse filter is described in detail in, e.g., "Fundamentals of Digital Image Processing", ANIL K. JAIN, pp. 275 to 277, Prentice-Hall International Editions.
According to this literature, as a reproducing filter, the following equation is given:
H.sup.- (.omega.)=1/H(.omega.) (2)
However, since this filter is represented by the reciprocal number of H(.omega.), when H(.omega.)=0 is satisfied, H.sup.- (.omega.) is diverged. Therefore, the following equations are defined: EQU H.sup.- (.omega.)=1/H(.omega.) (when H(.omega.).noteq.0) (3) EQU H.sup.- (.omega.)=0 (when H(.omega.)=0) (3')
In a reproducing filter represented by equations (2), (3), and (3'), an intensity distribution of the image of an optical system must be uniformed at any position of the image, i.e., PSFs in the image must be equal to each other (space-invariant).
However, in a practical optical system, since the PSFs are changed in accordance with their positions due to various aberrations, failure in focusing, or the like, the original image cannot be correctly reproduced by the reproducing filter represented by equations (2) and (3).
In this case, after the PSFs which are changed in accordance with their positions are correctly measured, the reproducing filter represented by equations (2) and (3) may be used. However, sampling of the PSFs performed prior to the measuring of the PSFs is posed as a problem.
That is, although an image on an observation image plane is defined as a continuous image, the image is separated into pixels in an image pickup element or the like, and the image is discretely sampled. Therefore, the PSFs cannot be correctly measured.
For this reason, it is essentially impossible to correctly reproduce an original image by a conventional reproducing filter.